Question

A half-adder is a device which adds 2 bits with no carry in. What is the truth table for outputs S (sum) and C (carry)?

a. S = A XOR B, C = A AND B
b. S = A AND B, C = A XOR B
c. S = A OR B, C = A AND B
d. S = A XOR B, C = A OR B

Answer 1

The truth table for a half-adder specifies that the sum (S) is obtained through an XOR operation and the carry (C) through an AND operation between two bits A and B. Therefore, the correct answer is 'S = A XOR B, C = A AND B'.

Step-by-step explanation:

The half-adder is a fundamental digital circuit that performs the addition of two single binary digits (bits). To answer the student's question, the truth table for a half-adder demonstrates how to get the outputs S (sum) and C (carry) when adding two bits A and B. Specifically, the sum (S) is the result of an XOR operation on A and B, and the carry (C) out is the result of an AND operation on A and B.

Here is the truth table for a half-adder:

• When A = 0 and B = 0, S (sum) = 0 XOR 0 = 0 and C (carry) = 0 AND 0 = 0
• When A = 0 and B = 1, S (sum) = 0 XOR 1 = 1 and C (carry) = 0 AND 1 = 0
• When A = 1 and B = 0, S (sum) = 1 XOR 0 = 1 and C (carry) = 1 AND 0 = 0
• When A = 1 and B = 1, S (sum) = 1 XOR 1 = 0 and C (carry) = 1 AND 1 = 1

So, the correct answer to the question: "What is the truth table for outputs S (sum) and C (carry) in a half-adder?" is "a. S = A XOR B, C = A AND B".